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Avoided crossings in mesoscopic systems: electron propagation on a non-uniform magnetic cylinder

Pavel Exner·Alain Joye
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Abstract

We consider an electron constrained to move on a surface with revolution symmetry in the presence of a constant magnetic field $B$ parallel to the surface axis. Depending on $B$ and the surface geometry the transverse part of the spectrum typically exhibits many crossings which change to avoided crossings if a weak symmetry breaking interaction is introduced. We study the effect of such perturbations on the quantum propagation. This problem admits a natural reformulation to which tools from molecular dynamics can be applied. In turn, this leads to the study of a perturbation theory for the time dependent Born-Oppenheimer approximation.

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Pavel Exner, Alain Joye. 2000-10-25. Avoided crossings in mesoscopic systems: electron propagation on a non-uniform magnetic cylinder. https://doi.org/10.1063/1.1396834

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